The present invention relates to a function element such as a light-modulating element or an LWI (Laser Without Inversion) laser which operates without population inversion, which operates by virtue of quantum interference effect in a solid.
Optical characteristics of a substance, such as absorption and emission, have been considered to be specific to the substance. In recent years, research has been widely conducted on the techniques of modulating the optical characteristics of substances by means of quantum interference effect. Quantum interference effect is a phenomenon in which, as shown in FIG. 1, absorption and emission intensify or weaken each other as two or more optical transitions simultaneously occur between two energy levels in substance.
Quantum interference effect involves in various optical phenomena. Among these optical phenomena are: electromagnetically induced transparency (EIT), described in J. Boller et al., Phys. Rev. Lett. 66, 2593 (1991); lasing without population inversion (LWI), disclosed in S. E. Harris, Phys. Rev. Lett. 62, 1033 (1989); enhancement of index of index of refraction, written in M. O. Scully, Phys. Rev. Lett. 67, 1855 (1991); and population trapping, disclosed in E. Arimondo et al., Lett. Nuovo Cimento, 17, 333 (1976). In EIT, light is not absorbed in substance, penetrating the substance, even if its wavelength falls within a high-absorption region. LWI enables a laser to oscillate without population inversion. Enhancement of refraction enables substance to acquire a large angle of diffraction. Population trapping confines electrons at a particular level even if excitation light is being applied to substance.
The optical phenomena mentioned above are not only novel and surprising from a scientific viewpoint, but also valuable from a technological viewpoint. Research is positively made to develop function elements, such as light-modulating elements and LWI lasers, to which quantum interference effect is applied.
Known as a method of artificially inducing a quantum interference effect is the EIT mentioned above. EIT is a phenomenon found when a laser beam is applied to atom gas. At the time it was found, the phenomenon was called "population trapping," not "EIT".
EIT and population trapping are one and the same phenomenon; "EIT" is a term emphasizing the resultant spectrum, while "population trapping" is a term accentuating the resultant distribution of electrons (see G. Alzping et al., Nuovo Cimento, B36, 5 (1976). Since 1978 when it was discovered, EIT has been observed in various atom-gas systems, as is disclosed in, for example, H. R. Gray et al., Opt. Lett. 3, 218 (1978); M. Kaivola et al., Opt. Commun., 49, 418 (1984); A. Aspect et al., Phys. Reve. Lett. 61, 826 (1988); S. Adachi et al., Opt. Commun., 81, 364 (1991); A. M. Akulsin et al., Opt. Commun., 84, 139 (1991); Y. Q. Li et al., Phys. Rev., A51, R1754 (1995); A. Kasapi et al., Phys. Rev. Lett. 74, 2447 (1995).
EIT may be applied in order to provide an LWI laser. An LWI laser in which atom gas is used will be described.
FIGS. 2A, 2B and 2C are schematic diagrams, each showing the energy levels of atom gas and the light beams applied to the atom gas. In a system equivalent to the LWI laser, atom gas may assume three energy levels and two coherent light beams (light 1 and light 2) are applied to atom gas to excite the gas. Three schemes exist, by virtue of level-light combination. FIGS. 2A, 2B and 2C shows the first scheme, second scheme and third scheme, respectively. In the first scheme (FIG. 2A) hereinafter referred to as ".LAMBDA.-type excitation", the highest level 1 is common level and two light beams excite the atom gas. In the second scheme (FIG. 2B) hereinafter referred to as "V-type excitation", the base level 3 is common level and two light beams excite the atom gas. In the third scheme (FIG. 2C) hereinafter referred to as ".XI.-type excitation", the intermediate level 2 is common level and two light beams excite the atom gas.
To induce a quantum interference effect in a system wherein .LAMBDA.-type excitation is performed, it is required that atom gas be forbidden from being excited from level 3 to level 2 (level 2 is in metastable state) and that the relaxation speed be zero.
This requirement is one of the two conditions for inducing a quantum interference effect by virtue of EIT. It is known as a condition for quantum interference, relating to transition probability and relaxation.
Assume that the absorption spectrum of the beam 2 is examined, while changing the photon energy .omega..sub.1 of the light beam 1, under the condition of .delta..omega..sub.1 =.omega..sub.1 -.omega..sub.12 =0, that is, the photon energy .omega..sub.1 of the light beam 1 equals the energy .omega..sub.12 between the levels 1 and 2. FIG. 3A shows the absorption spectrum of the light beam 2. In FIG. 3A, the value .delta..omega..sub.2 plotted on the ordinate is modified by the detuning between the photon energy .omega..sub.2 of the light beam 2 and the energy .omega..sub.13 between the levels 1 and 3. That is, .delta..omega..sub.2 =.omega..sub.2 -.omega..sub.13.
As seen from FIG. 3A, the absorption spectrum, which should have a single peak, has an absorption hole (i.e., a transparent region) when .delta..omega..sub.2 =0 (=.delta..omega..sub.1). Equation of .delta..omega..sub.2=.delta..omega..sub.1 is the other of the two conditions for inducing a quantum interference effect by virtue of EIT, or the condition relating to the detuning.
The transparent region in the absorption spectrum has a width of .OMEGA.=(.OMEGA..sub.1.sup.2 -.OMEGA..sub.2.sup.2).sup.1/2, where .OMEGA..sub.1 is the Rabi frequency of the light beam 1 and .OMEGA..sub.2 is the Rabi frequency of the light beam 2.
Rabi frequency .OMEGA..sub.12 is the strength of interaction between substance and light beam 1 whose Rabi frequency .OMEGA..sub.1 is expressed as 2.pi..mu..sub.12 E.sub.1 /h, where .mu..sub.12 is the electric dipole moment between levels 1 and 2, E.sub.1 is the electric-field intensity of the light beam 1, and h is Planck's constant. Rabi frequency .OMEGA..sub.13 is the strength of interaction between substance and light beam 2 whose Rabi frequency .OMEGA..sub.2 is expressed as 2.pi..mu..sub.13 E.sub.2 /h, where .mu..sub.13 is the electric dipole moment between levels 1 and 3, E.sub.2 is the electric-field intensity of the light beam 1, and h is Planck's constant.
FIG. 3B shows the absorption spectrum of the light beam 2 observed when the photon energy of the light beam 1 is set in the state of .delta..omega..sub.1 =.delta..omega..sub.2 =0. As can be understood from FIG. 3B, the absorption spectrum has a transparent region at the skirt where .delta..omega..sub.1 =.delta..omega..sub.2, which light is not absorbed at all. The transparent region has a width of .OMEGA.=(.OMEGA..sub.1.sup.2 -.OMEGA..sub.2.sup.2 +.delta..omega..sub.2.sup.2).sup.1/2.
As described above, in the case of EIT, even light that must be greatly absorbed will no longer be absorbed if two light beams are applied. The reason why such light is not absorbed can be explained from dressed-state diagrams.
FIG. 4 illustrates how the natural state of atoms changes as the light beam 1 acts between levels 1 and 2. The levels shown in the left half of FIG. 4 are energy levels a bare atom may have, whereas the levels shown in the right half of FIG. 4 are energy levels a dressed atom may have.
The highest level 1 splits into two nearly degenerate levels for a dressed atom, i.e., an atom on which the light beam 1 acts. The nearly degenerate levels assume a dressed-state. The energy of the atom gas can be raised from the base level 3 to these nearly degenerate levels when one light beam (beam 2) is applied to the atom gas.
The light beam 2 ceases to be absorbed. This phenomenon may be considered to have been caused because two energy transitions from level 3 to two other close levels interfere with each other. Namely, the two energy transitions weaken each other. This interference effect can be caused by other types of excitation, i.e., V-type excitation and .XI.-type excitation. In whichever type of excitation, the mechanism of forming a transparent region in the spectrum can be well explained by the theoretical curve obtained by, for example, analyzing the density matrix.
An LWI laser developed on the basis of EIT may assume one of the three schemes, i.e., .LAMBDA.-type excitation, V-type excitation and .XI.-type excitation, depending on the combination of the energy level and the light beam. Here again, .LAMBDA.-type excitation will be discussed.
FIG. 5 is a schematic representation of the energy levels of atom gas and the light beams applied to the atom gas. The light beam 3 applied in addition to light beams 1 and 2 is an incoherent beam for pumping electrons from the ground level to a higher level.
Assume that the coherent light beams 1 and 2 applied to this system satisfy the interference condition with respect to detuning and that the atom gas assumes a quantum interference state and does not absorb the light beam 2. When the incoherent light beam 3 is applied to the system, it is absorbed in the system. This is because the interference effect resulting from EIT does not act on any incoherent light, whereby an energy transition occurs from level 3 to level 1. An incoherent light beam may be regarded as having a broad spectral width that is greater than the width of the transparent region resulting from quantum interference.
In EIT, the interference effect does not work to cause emission. The energy transition between levels 1 and 3, which assumes a quantum interference state, has an asymmetric absorption-emission characteristic. Only emission can take place, particularly in the transparent region.
Electrons excited by the light beam 1 to level 1 fall back to level 3 due to induced radiation caused by the light beam 2. The coherent light beam 2 can be amplified even if the population at level 1 is smaller than the population at level 3 which is lower than level 1, that is, even if the distribution of electrons is not inverted. This amplification, therefore, attracts attention as a principle of laser oscillation.
To provide an LWI laser it suffices to place the system of FIG. 5 in a resonator, apply only the light beam 1 (i.e., a coherent light beam) and pump, by some a method, the electrons from the base level into an excited state. If so, a laser oscillation gain is obtained at a photon energy of about (.omega..sub.1 -.omega..sub.23), where .omega..sub.1 is the photon energy of the light beam 1 which excites the atom gas from level 1 to level 2 and .omega..sub.23 is the transition energy between levels 2 and 3. As a result, coherent light is generated. The mechanism of the laser oscillation achieved without inverting the electron distribution can be explained by analyzing the density matrix, as is the mechanism of EIT.
.LAMBDA.-type excitation has been described with reference to FIG. 5. V-type excitation and .XI.-type excitation can also be applied to LWI lasers, as is proved by the analysis of density matrices.
As can be understood from the above description of EIT, it is possible to induce a quantum interference effect in a solid system. Hence, there can be provided a light-modulating element which can operate with weak light and which may, therefore, replace the existing light-modulating element utilizing nonlinear optics and unable to operate with weak light. Further, an LWI laser can be provided which oscillates at a low threshold value in a short-wave region. Moreover, quantum interference may be combined with the various physical properties of a solid, such as electrical conduction, magnetic property and dielectric property, to create a novel function element which differs from the existing electric elements.
However, the following difficulties involve in applying EIT to solid systems.
First, since the interference of the optical transitions between particular energy levels is utilized in EIT, it is difficult to use such an energy level as will form a band. Research is are made in order to accomplish perfect zero-absorption by means of EIT, by using semiconductor quantum wells or impurities whose energy is relatively discrete in solids. See, for example, A. Imamoglu et al., Opt. Lett. 19, 1744 (1994); P. J. Harshman et al., IEEE J. Quantum Electronics, 30, 2297 (1994); D. Huang et al., J. Opt. Soc. Am., B11, 2297 (1994); Y. Zhu et al., Phys. Rev., A49, 4016 (1994).
However, no such prominent light modulation as is observed in atom gas systems has thus far been obtained in solid systems. Some reports show that absorption did reduce, but at temperatures as low as liquid helium temperature. See H. Schmidt et al., Appl. Phys. Lett. 70, 3455 (1997); Y. Zhao et al., Phys. Rev. Lett. 79, 641 (1997): B. S. Ham et al., Opt. Lett. 22, 1138 (1997).
Why no prominent light modulation has occurred in solid systems? There seem to be two reasons. First, relaxation proceeds fast in solid systems. Second, optical transition has a great inhomogeneous broadening in solid systems.
In the case of EIT of .LAMBDA.-type excitation, it is required that, as described above, excitation between level 2 (intermediate level) and level 3 (base level) be forbidden and that level 2 be in metastable state, remaining unchanged for a long time. It is further required that two light beams be equal in terms of detuning. In view of these requirements, the inhomogenous broadening of the transition must be less than the homogenous broadening thereof or Rabi frequency.
Even in a semiconductor quantum well system or impurity systems whose characteristic is relatively similar to that of atomic system, it is extremely difficult to find a three-level system having no inhomogeneous broadening and including one excited level that would not be relaxed. This may be the reason why no function element has ever been provided that has prominent light-modulating characteristic by virtue of EIT.